{"id":14339,"date":"2025-01-12T20:52:27","date_gmt":"2025-01-12T23:52:27","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=14339"},"modified":"2025-01-23T01:59:37","modified_gmt":"2025-01-23T04:59:37","slug":"water-reflexive-magic-squares-order-11-to-15","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=14339","title":{"rendered":"Water Reflection Magic Squares: Orders 11 to 13"},"content":{"rendered":"\n<p>This work brings more concepts in magic squares. In past we studied a lot of upside-down and mirror looking magic squares. These are based some kind of digital\/special fonts. To understand better let&#8217;s consider the following 10 digits from 0 to 9:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-1024x90.png\" alt=\"\" class=\"wp-image-14128\" style=\"width:699px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-9bb23a63a92f5e66e4d5ab76f26113f0\">Upside-down<strong> (180 degrees rotation)<\/strong><\/h4>\n\n\n\n<p>Let&#8217;s make 180 degrees rotation over the above 10 digits, we get<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-1024x90.png\" alt=\"\" class=\"wp-image-14130\" style=\"width:691px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>We observe that the numbers 0, 1, 2, 5, 6, 8 and 9 are still there. The difference is that 6 becomes 9.<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-6254d61d65daf44d6885af59f4408f5c\">Mirror Looking (Horizontal Flip)<\/h4>\n\n\n\n<p>Let&#8217;s see how these numbers can seen in mirror:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-1024x90.png\" alt=\"\" class=\"wp-image-14129\" style=\"width:698px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>We observe that the numbers 0, 1, 2, 5 and 8 are still there. In this case the numbers 2 and 5 interchanges, i.e., 2 becomes 5 and 5 as 2.<\/p>\n\n\n\n<p>In general there are two kinds of flips, i.e.,<strong> horizontal flip<\/strong> and <strong>vertical filp<\/strong>. See the image below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"278\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/flip.png\" alt=\"\" class=\"wp-image-14131\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/flip.png 354w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/flip-300x236.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-right\">Source: <a href=\"https:\/\/www.mathsisfun.com\/definitions\/vertical-flip.html\">https:\/\/www.mathsisfun.com\/definitions\/vertical-flip.html<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-bf7d1a8f7075e9d1cc6bb9fb0b25506a\">Water Reflection (Vertical Flip)<\/h4>\n\n\n\n<p>Making vertical flip over the digits 0 to 9, we get<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-1024x90.png\" alt=\"\" class=\"wp-image-14132\" style=\"width:700px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>We observe the numbers 0, 1, 2, 3, 5 and 8 remains the same. The numebrs 0, 1, 2, 5 and 8 are already in mirror looking except the number. That&#8217;s why we call these numbers as <strong>universal<\/strong> numbers.  Here also 2 becomes 5 and 5 as 2. Thus using <strong>vertical flip<\/strong>, we get an extra number as 3. Let&#8217;s call the operation as <strong>water reflection<\/strong>. This means that the numbers 0, 1, 2, 3, 5 and 8 are <strong>water reflexive<\/strong>.<\/p>\n\n\n\n<p>The aim this work is write magic squares based on the numbers 0, 1, 2, 3, 5 and 8, where 3 is always there, i.e., making combinations of 3 with the numbers 0, 1, 2, 5 and 8. This work is for orders 11 to 13. See the details of this work<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 38%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Magic Squares of Order 11<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 1. Magic Square with 4-Digits (2,3,5,8)<\/li>\n\n\n\n<li>Example 2. Magic Square with 4-Digits (1,2,3,5)<\/li>\n\n\n\n<li>Example 3. Magic Squares with 4-Digits (0,2,3,5)<\/li>\n\n\n\n<li>Example 4. Magic Squares with 4-Digits (0,1,3,8)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 6-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 5. Magic Square with 3-Digits (2,3,5)<\/li>\n\n\n\n<li>Example 6. Magic Square with 3-Digits (1,3,8)<\/li>\n\n\n\n<li>Example 7. Magic Square with 3-Digits (0,3,8)<\/li>\n\n\n\n<li>Example 8. Magic Square with 3-Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>c) 8-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 9. Magic Square with 2-Digits (3,8)<\/li>\n\n\n\n<li>Example 10. Magic Square with 3-Digits (1,3)<\/li>\n\n\n\n<li>Example 11. Magic Square with 3-Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 12: Blocks of Magic Squares of Order 4<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 12. Magic Square with 4-Digits (2,3,5,8)<\/li>\n\n\n\n<li>Example 13. Magic Square with 4-Digits (1,2,3,5)<\/li>\n\n\n\n<li>Example 14. Magic Square with 4-Digits (0,2,3,5)<\/li>\n\n\n\n<li>Example 15. Magic Square with 4-Digits (0,1,3,8)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 6-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 16. The Digits (2,3,5)<\/li>\n\n\n\n<li>Example 17. The Digits (1,3,8)<\/li>\n\n\n\n<li>Example 18. The Digits (0,3,8)<\/li>\n\n\n\n<li>Example 19. The Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>c) 8-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 20. The Digits (3,8)<\/li>\n\n\n\n<li>Example 21. The Digits (1,3)<\/li>\n\n\n\n<li>Example 22. The Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 12: Blocks of Semi-Magic Squares of Order 3<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 23. The 4-Digits (2,3,5,8)<\/li>\n\n\n\n<li>Example 24. The 4-Digits (1,2,3,5)<\/li>\n\n\n\n<li>Example 25. The 4-Digits (0,2,3,5)<\/li>\n\n\n\n<li>Example 26. 4-The Digits (0,1,3,8)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 6-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 27. The 3-Digits (2,3,5)<\/li>\n\n\n\n<li>Example 28. The 3-Digits (1,3,8)<\/li>\n\n\n\n<li>Example 29. The 3-Digits (0,3,8)<\/li>\n\n\n\n<li>Example 30. The 3-Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 8-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 31. The 2-Digits (3,8)<\/li>\n\n\n\n<li>Example 32. The 2-Digits (1,3)<\/li>\n\n\n\n<li>Example 33. The 2-Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 13<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 34. The 4-Digits (2,3,5,8)<\/li>\n\n\n\n<li>Example 35. The 4-Digits (1,2,3,5)<\/li>\n\n\n\n<li>Example 36. The 4-Digits (0,2,3,5)<\/li>\n\n\n\n<li>Example 37. The 4-Digits (0,1,3,8)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 6-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 38. The 3-Digits (2,3,5)<\/li>\n\n\n\n<li>Example 39. The 3-Digits (1,3,8)<\/li>\n\n\n\n<li>Example 40. The 3-Digits (0,3,8)<\/li>\n\n\n\n<li>Example 41. The 3-Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 8-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 42. The 2-Digits (3,8)<\/li>\n\n\n\n<li>Example 43. The 2-Digits (1,3)<\/li>\n\n\n\n<li>Example 44. The 2-Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>References<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Full work can be downloaded from the following link:<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(244,250,200) 57%,rgb(169,184,195) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja, <\/strong><em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 11 to 13<\/em>, <strong>Zenodo<\/strong>, January 15, 2025, pp. 1-146, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14649320\">https:\/\/doi.org\/10.5281\/zenodo.14649320<\/a>.<\/li>\n<\/ul>\n\n\n\n<p>For the previous work on orders 3 to 10 refer the links below. The link of this work is also there.<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(244,250,200) 57%,rgb(169,184,195) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja, <\/strong><a href=\"https:\/\/numbers-magic.com\/?p=14126\">Water Reflection Magic Squares: Order 3 to 6<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14213\">Water Reflection Magic Squares: Order 7 to 10. <\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14339\">Water Reflection Magic Squares: Order 11 to 13.<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(212,193,193) 22%,rgb(18,184,20) 57%,rgb(237,212,212) 74%,rgb(113,206,126) 100%)\">Magic Squares of Order 11<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-b3fd78649fe4d2408410d66cfcf938a5\">a) 4-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-86441fee1104cc32459d94699ef3e079\">Example 1. Magic Square with 4-Digits (2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1078\" height=\"499\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358.png\" alt=\"\" class=\"wp-image-14340\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358.png 1078w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358-1024x474.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358-535x248.png 535w\" sizes=\"(max-width: 1078px) 100vw, 1078px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1078\" height=\"499\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358w.png\" alt=\"\" class=\"wp-image-14341\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358w.png 1078w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358w-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358w-1024x474.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358w-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-2358w-535x248.png 535w\" sizes=\"(max-width: 1078px) 100vw, 1078px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-7b8a73de64f8eaf8c311299de73bac20\">Example 2. Magic Square with 4-Digits (1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1076\" height=\"499\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235.png\" alt=\"\" class=\"wp-image-14345\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235.png 1076w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235-1024x475.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235-535x248.png 535w\" sizes=\"(max-width: 1076px) 100vw, 1076px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1076\" height=\"499\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235w.png\" alt=\"\" class=\"wp-image-14344\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235w.png 1076w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235w-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235w-1024x475.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235w-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-1235w-535x248.png 535w\" sizes=\"(max-width: 1076px) 100vw, 1076px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-55519ad3a1b574f882ad73b16056856a\">Example 3. Magic Squares with 4-Digits (0, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1079\" height=\"502\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235.png\" alt=\"\" class=\"wp-image-14352\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235.png 1079w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235-300x140.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235-1024x476.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235-768x357.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235-535x249.png 535w\" sizes=\"(max-width: 1079px) 100vw, 1079px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1079\" height=\"502\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235w.png\" alt=\"\" class=\"wp-image-14353\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235w.png 1079w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235w-300x140.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235w-1024x476.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235w-768x357.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0235w-535x249.png 535w\" sizes=\"(max-width: 1079px) 100vw, 1079px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-e019b6ce683d50918ee737579ac5f551\">Example 4. Magic Squares with 4-Digits (0,1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"930\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138.png\" alt=\"\" class=\"wp-image-14348\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138.png 930w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138-300x169.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138-768x433.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138-535x301.png 535w\" sizes=\"(max-width: 930px) 100vw, 930px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"930\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138w.png\" alt=\"\" class=\"wp-image-14349\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138w.png 930w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138w-300x169.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138w-768x433.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-0138w-535x301.png 535w\" sizes=\"(max-width: 930px) 100vw, 930px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflection pandiagonal magic<\/strong> squares of order 11 having <strong>4-digits cells entries<\/strong> with four number combinations (2,3,5,8), (1,2,3,5), (0,2, 5, 8) and, (0,1,3,8).<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-fc76ea2193f8773edb397f7f823a4610\">b) 6-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-89805a61605c1b28ab43a0035b88122c\">Example 5. Magic Square with 3-Digits (2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1448\" height=\"501\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235.png\" alt=\"\" class=\"wp-image-14354\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235.png 1448w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235-300x104.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235-1024x354.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235-768x266.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235-535x185.png 535w\" sizes=\"(max-width: 1448px) 100vw, 1448px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1448\" height=\"501\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235w.png\" alt=\"\" class=\"wp-image-14355\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235w.png 1448w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235w-300x104.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235w-1024x354.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235w-768x266.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-235w-535x185.png 535w\" sizes=\"(max-width: 1448px) 100vw, 1448px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6f6f7cddefe6d806467b83591f2e2b7a\">Example 6. Magic Square with 3-Digits (1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1229\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138-1.png\" alt=\"\" class=\"wp-image-14356\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138-1.png 1229w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138-1-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138-1-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138-1-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138-1-535x228.png 535w\" sizes=\"(max-width: 1229px) 100vw, 1229px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1229\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138w.png\" alt=\"\" class=\"wp-image-14357\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138w.png 1229w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138w-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138w-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138w-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-138w-535x228.png 535w\" sizes=\"(max-width: 1229px) 100vw, 1229px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6499c6cc2c5f20ab7fec4310f5697606\">Example 7. Magic Square with 3-Digits (0, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1229\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038.png\" alt=\"\" class=\"wp-image-14359\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038.png 1229w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038-535x228.png 535w\" sizes=\"(max-width: 1229px) 100vw, 1229px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1229\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038w.png\" alt=\"\" class=\"wp-image-14360\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038w.png 1229w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038w-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038w-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038w-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-038w-535x228.png 535w\" sizes=\"(max-width: 1229px) 100vw, 1229px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-9f4ffd8602a25778ac01140a1c45796e\">Example 8. Magic Square with 3-Digits (0, 1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1227\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013.png\" alt=\"\" class=\"wp-image-14364\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013.png 1227w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013-768x328.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013-535x228.png 535w\" sizes=\"(max-width: 1227px) 100vw, 1227px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1227\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013w-1.png\" alt=\"\" class=\"wp-image-14363\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013w-1.png 1227w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013w-1-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013w-1-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013w-1-768x328.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-013w-1-535x228.png 535w\" sizes=\"(max-width: 1227px) 100vw, 1227px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflection pandiagonal <\/strong>magic squares of order 11 having<strong> 6-digits cells entries<\/strong> with three numbers combinations (2, 3, 5), (1, 3, 8), (0,3,8) and, (0, 1, 3).<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-d15a2831c10df8655df53d4a90bd1e2f\">c) 8-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0f27b05c390572282c093b1913662f11\">Example 9. Magic Square with 2-Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1361\" height=\"501\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38.png\" alt=\"\" class=\"wp-image-14369\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38.png 1361w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38-1024x377.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38-535x197.png 535w\" sizes=\"(max-width: 1361px) 100vw, 1361px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1361\" height=\"501\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38w-1.png\" alt=\"\" class=\"wp-image-14368\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38w-1.png 1361w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38w-1-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38w-1-1024x377.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38w-1-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-38w-1-535x197.png 535w\" sizes=\"(max-width: 1361px) 100vw, 1361px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-4f1451cc9a31d7e65c340c2ca5d78b97\">Example 10. Magic Square with 3-Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1358\" height=\"501\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13.png\" alt=\"\" class=\"wp-image-14370\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13.png 1358w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13-300x111.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13-1024x378.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13-535x197.png 535w\" sizes=\"(max-width: 1358px) 100vw, 1358px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1358\" height=\"501\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13w.png\" alt=\"\" class=\"wp-image-14371\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13w.png 1358w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13w-300x111.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13w-1024x378.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13w-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-13w-535x197.png 535w\" sizes=\"(max-width: 1358px) 100vw, 1358px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-d1d5cc41d069ea5e47c1430d90c1ed4f\">Example 11. Magic Square with 3-Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1360\" height=\"502\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03.png\" alt=\"\" class=\"wp-image-14372\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03.png 1360w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03-300x111.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03-1024x378.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03-535x197.png 535w\" sizes=\"(max-width: 1360px) 100vw, 1360px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1360\" height=\"502\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03w-1.png\" alt=\"\" class=\"wp-image-14402\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03w-1.png 1360w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03w-1-300x111.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03w-1-1024x378.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03w-1-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/11x11-03w-1-535x197.png 535w\" sizes=\"(max-width: 1360px) 100vw, 1360px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflection pandiagonal <\/strong>magic squares of order 11 having<strong> 8-digits cells entries<\/strong> with two numbers combinations (3, 8), (1, 3) and, (0, 3).<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(212,193,193) 22%,rgb(18,184,20) 57%,rgb(237,212,212) 74%,rgb(113,206,126) 100%)\">Magic Squares of Order 12: <br>Blocks of Magic Squares of Order 4<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-b3fd78649fe4d2408410d66cfcf938a5\">a) 4-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-9207770c85945aa1e3c06502b6fa67aa\">Example 12. Magic Square with 4-Digits (2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1187\" height=\"550\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358.png\" alt=\"\" class=\"wp-image-14374\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358.png 1187w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358-1024x474.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358-535x248.png 535w\" sizes=\"(max-width: 1187px) 100vw, 1187px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1187\" height=\"550\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358w.png\" alt=\"\" class=\"wp-image-14375\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358w.png 1187w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358w-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358w-1024x474.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358w-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-2358w-535x248.png 535w\" sizes=\"(max-width: 1187px) 100vw, 1187px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-141b17e5cb1261b66aed45be20d1ec71\">Example 13. Magic Square with 4-Digits (1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1172\" height=\"552\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235.png\" alt=\"\" class=\"wp-image-14376\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235.png 1172w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235-300x141.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235-1024x482.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235-768x362.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235-535x252.png 535w\" sizes=\"(max-width: 1172px) 100vw, 1172px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1172\" height=\"552\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235w.png\" alt=\"\" class=\"wp-image-14378\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235w.png 1172w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235w-300x141.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235w-1024x482.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235w-768x362.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235w-535x252.png 535w\" sizes=\"(max-width: 1172px) 100vw, 1172px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6b5e289321d40fd94fabf51740d35c71\">Example 14. Magic Square with 4-Digits (0, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1189\" height=\"550\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235.png\" alt=\"\" class=\"wp-image-14379\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235.png 1189w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235-1024x474.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235-768x355.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235-535x247.png 535w\" sizes=\"(max-width: 1189px) 100vw, 1189px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1189\" height=\"550\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235w.png\" alt=\"\" class=\"wp-image-14381\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235w.png 1189w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235w-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235w-1024x474.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235w-768x355.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0235w-535x247.png 535w\" sizes=\"(max-width: 1189px) 100vw, 1189px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-fa587bf6efc51e125957cf10470934ae\">Example 15. Magic Square with 4-Digits (0, 1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1014\" height=\"577\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138.png\" alt=\"\" class=\"wp-image-14383\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138.png 1014w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138-300x171.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138-768x437.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138-535x304.png 535w\" sizes=\"(max-width: 1014px) 100vw, 1014px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1014\" height=\"577\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138w.png\" alt=\"\" class=\"wp-image-14380\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138w.png 1014w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138w-300x171.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138w-768x437.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-0138w-535x304.png 535w\" sizes=\"(max-width: 1014px) 100vw, 1014px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Total there are four<strong> water reflection<\/strong> magic squares. Out of them three <strong>semi-magic<\/strong> squares of order 12 having <strong>4-digits cells entries<\/strong> with four numbers combinations (2, 3, 5, 8), (1, 2, 3, 5) and (0,1, 3, 8). The blocks of order 4 are <strong>magic squares<\/strong> of order 4 with different magic sums. The one with 4-digits (0, 2, 3, 5) is magic squares with blocks of order 4 are <strong>pandiagonal<\/strong> magic squares with equal magic sums.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-fc76ea2193f8773edb397f7f823a4610\">b) 6-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-5034ab748f6901bf1dfb7f84c941d1c9\">Example 16. The Digits (2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1324\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235.png\" alt=\"\" class=\"wp-image-14384\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235.png 1324w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235-300x126.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235-1024x428.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235-768x321.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235-535x224.png 535w\" sizes=\"(max-width: 1324px) 100vw, 1324px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1324\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235w.png\" alt=\"\" class=\"wp-image-14385\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235w.png 1324w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235w-300x126.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235w-1024x428.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235w-768x321.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-235w-535x224.png 535w\" sizes=\"(max-width: 1324px) 100vw, 1324px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-ad4fc2d82a3ac7db16ce7f666928dd09\">Example 17. The Digits (1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1340\" height=\"579\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138.png\" alt=\"\" class=\"wp-image-14386\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138.png 1340w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138-1024x442.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138-535x231.png 535w\" sizes=\"(max-width: 1340px) 100vw, 1340px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1340\" height=\"579\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138w.png\" alt=\"\" class=\"wp-image-14387\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138w.png 1340w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138w-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138w-1024x442.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138w-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-138w-535x231.png 535w\" sizes=\"(max-width: 1340px) 100vw, 1340px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-9453ac830227ef56ece17d236408462a\">Example 18. The Digits (0, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1342\" height=\"577\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038.png\" alt=\"\" class=\"wp-image-14388\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038.png 1342w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038-300x129.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038-1024x440.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038-768x330.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038-535x230.png 535w\" sizes=\"(max-width: 1342px) 100vw, 1342px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1342\" height=\"577\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038w.png\" alt=\"\" class=\"wp-image-14389\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038w.png 1342w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038w-300x129.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038w-1024x440.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038w-768x330.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-038w-535x230.png 535w\" sizes=\"(max-width: 1342px) 100vw, 1342px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-3b5b5793557df09632abae36c8e5cebc\">Example 19. The Digits (0, 1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1339\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013.png\" alt=\"\" class=\"wp-image-14390\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013.png 1339w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013-1024x444.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013-768x333.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013-535x232.png 535w\" sizes=\"(max-width: 1339px) 100vw, 1339px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1339\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013w.png\" alt=\"\" class=\"wp-image-14391\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013w.png 1339w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013w-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013w-1024x444.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013w-768x333.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-013w-535x232.png 535w\" sizes=\"(max-width: 1339px) 100vw, 1339px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflection semi-magic<\/strong> squares of order 12 having <strong>6-digits cells entries<\/strong> with three numbers combinations (2,3,5), (1,3, 8), (0, 3, 8) and (0,1, 3). The blocks of order 4 are different sums magic squares of order 4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-d15a2831c10df8655df53d4a90bd1e2f\">c) 8-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6ad518aa4aea428e1b10cab54a917bd3\">Example 20. The Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1482\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38.png\" alt=\"\" class=\"wp-image-14394\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38.png 1482w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38-1024x383.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38-768x287.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38-535x200.png 535w\" sizes=\"(max-width: 1482px) 100vw, 1482px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1482\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38w.png\" alt=\"\" class=\"wp-image-14395\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38w.png 1482w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38w-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38w-1024x383.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38w-768x287.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-38w-535x200.png 535w\" sizes=\"(max-width: 1482px) 100vw, 1482px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-c227b1deea862597aafa7492aebca9a3\">Example 21. The Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1479\" height=\"556\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13.png\" alt=\"\" class=\"wp-image-14396\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13.png 1479w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13-300x113.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13-1024x385.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13-768x289.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13-535x201.png 535w\" sizes=\"(max-width: 1479px) 100vw, 1479px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1479\" height=\"556\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13w.png\" alt=\"\" class=\"wp-image-14397\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13w.png 1479w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13w-300x113.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13w-1024x385.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13w-768x289.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-13w-535x201.png 535w\" sizes=\"(max-width: 1479px) 100vw, 1479px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-bb563554c110ab27c1af7bac4b681457\">Example 22. The Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1484\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03.png\" alt=\"\" class=\"wp-image-14398\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03.png 1484w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03-1024x382.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03-768x287.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03-535x200.png 535w\" sizes=\"(max-width: 1484px) 100vw, 1484px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1484\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03w.png\" alt=\"\" class=\"wp-image-14399\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03w.png 1484w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03w-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03w-1024x382.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03w-768x287.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-03w-535x200.png 535w\" sizes=\"(max-width: 1484px) 100vw, 1484px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflection pandiagonal <\/strong>magic squares of order 12 having <strong>8-digits cells entries<\/strong> with two numbers combinations (3,8), (1,3) and (0, 3). The blocks of order 4 are also <strong>pandiagonal<\/strong> magic squares of order 4 with equal magic sums.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(212,193,193) 22%,rgb(18,184,20) 57%,rgb(237,212,212) 74%,rgb(113,206,126) 100%)\">Magic Squares of Order 12:<br>Blocks of Semi-Magic Squares of Order 3<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-60a89780fdb35a1d79d4ce75650cd8dd\">a) 4-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-34fd7fbabe6161eb5d8e154b0213e194\">Example 23. The 4-Digits (2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1189\" height=\"555\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358.png\" alt=\"\" class=\"wp-image-14403\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358.png 1189w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358-300x140.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358-1024x478.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358-768x358.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358-535x250.png 535w\" sizes=\"(max-width: 1189px) 100vw, 1189px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1189\" height=\"555\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358w.png\" alt=\"\" class=\"wp-image-14404\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358w.png 1189w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358w-300x140.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358w-1024x478.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358w-768x358.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-2358w-535x250.png 535w\" sizes=\"(max-width: 1189px) 100vw, 1189px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-ec755827fbfad7bb98bc260e7248474b\">Example 24. The 4-Digits (1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1168\" height=\"552\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235.png\" alt=\"\" class=\"wp-image-14405\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235.png 1168w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235-300x142.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235-1024x484.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235-768x363.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235-535x253.png 535w\" sizes=\"(max-width: 1168px) 100vw, 1168px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1168\" height=\"552\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235w.png\" alt=\"\" class=\"wp-image-14406\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235w.png 1168w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235w-300x142.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235w-1024x484.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235w-768x363.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-1235w-535x253.png 535w\" sizes=\"(max-width: 1168px) 100vw, 1168px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-ed7584792ab661bbae8f0541967e0d30\">Example 25. The 4-Digits (0, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1194\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235.png\" alt=\"\" class=\"wp-image-14407\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235.png 1194w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235-1024x475.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235-535x248.png 535w\" sizes=\"(max-width: 1194px) 100vw, 1194px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1194\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235w.png\" alt=\"\" class=\"wp-image-14408\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235w.png 1194w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235w-300x139.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235w-1024x475.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235w-768x356.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0235w-535x248.png 535w\" sizes=\"(max-width: 1194px) 100vw, 1194px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-75e4059f39c94813dab8ef31baa7527f\">Example 26. 4-The Digits (0, 1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1015\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138.png\" alt=\"\" class=\"wp-image-14409\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138.png 1015w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138-300x171.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138-768x439.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138-535x306.png 535w\" sizes=\"(max-width: 1015px) 100vw, 1015px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1015\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138w.png\" alt=\"\" class=\"wp-image-14410\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138w.png 1015w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138w-300x171.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138w-768x439.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-0138w-535x306.png 535w\" sizes=\"(max-width: 1015px) 100vw, 1015px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Total we have four magic squares. Out of  them three examples are <strong>water reflexive semi-magic<\/strong> squares of order 12 having <strong>4-digits cells entries<\/strong> with 4 numbers combinations (2, 3, 5, 8), (1, 2, 3, 5) and (0, 1, 3, 8). The blocks of order 3 are also <strong>semi-magic<\/strong> squares of order 3 with different <strong>semi-magic<\/strong> sums. <br><br>The only one magic square of order 12 with digits (0, 2, 3, 5) is <strong>pandiagonal<\/strong>, but the blocks of order 3 are <strong>semi-magic<\/strong> square with different <strong>semi-magic<\/strong> sums, but the <strong>water reflection<\/strong> property in this case is <strong>semi-magic<\/strong> square of order 12.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-ec61b07d51a39014f30f38c3524f9bd3\">b) 6-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-84ba7e01e93f2afcd41747fab5deccc6\">Example 27. The 3-Digits (2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1327\" height=\"558\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235.png\" alt=\"\" class=\"wp-image-14411\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235.png 1327w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235-300x126.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235-1024x431.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235-768x323.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235-535x225.png 535w\" sizes=\"(max-width: 1327px) 100vw, 1327px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1327\" height=\"558\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235w.png\" alt=\"\" class=\"wp-image-14412\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235w.png 1327w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235w-300x126.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235w-1024x431.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235w-768x323.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-235w-535x225.png 535w\" sizes=\"(max-width: 1327px) 100vw, 1327px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-2dfeba94a2cb3426ee6a58e03ef684be\">Example 28. The 3-Digits (1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1343\" height=\"582\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138.png\" alt=\"\" class=\"wp-image-14413\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138.png 1343w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138-1024x444.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138-768x333.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138-535x232.png 535w\" sizes=\"(max-width: 1343px) 100vw, 1343px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1343\" height=\"582\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138w.png\" alt=\"\" class=\"wp-image-14414\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138w.png 1343w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138w-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138w-1024x444.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138w-768x333.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-138w-535x232.png 535w\" sizes=\"(max-width: 1343px) 100vw, 1343px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-7cb6060c46b3e996bebf6db418f3a228\">Example 29. The 3-Digits (0, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1343\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038.png\" alt=\"\" class=\"wp-image-14415\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038.png 1343w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038-1024x442.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038-535x231.png 535w\" sizes=\"(max-width: 1343px) 100vw, 1343px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1343\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038w.png\" alt=\"\" class=\"wp-image-14416\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038w.png 1343w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038w-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038w-1024x442.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038w-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-038w-535x231.png 535w\" sizes=\"(max-width: 1343px) 100vw, 1343px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-f7614fae5809497d791703427b8ab171\">Example 30. The 3-Digits (0, 1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1340\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013.png\" alt=\"\" class=\"wp-image-14417\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013.png 1340w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013-1024x443.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013-535x232.png 535w\" sizes=\"(max-width: 1340px) 100vw, 1340px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1340\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013w.png\" alt=\"\" class=\"wp-image-14418\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013w.png 1340w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013w-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013w-1024x443.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013w-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-013w-535x232.png 535w\" sizes=\"(max-width: 1340px) 100vw, 1340px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflexive<\/strong> <strong>semi-magic<\/strong> squares of order 12 having <strong>6-digits cells entries<\/strong> with 3 numbers combinations (2, 3, 5), (1, 3, 8), (0, 3, 8) and (0, 1, 3). The blocks of order 3 are also <strong>semi-magic<\/strong> squares of order 3 with different <strong>semi-magic<\/strong> sums.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3077b9d4db17c7dbc5623348fb3d851c\">b) 8-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-8a0cfbc40cfacc1be6f041ef7e30f50a\">Example 31. The 2-Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1485\" height=\"553\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38.png\" alt=\"\" class=\"wp-image-14419\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38.png 1485w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38-1024x381.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38-768x286.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38-535x199.png 535w\" sizes=\"(max-width: 1485px) 100vw, 1485px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1485\" height=\"553\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38w.png\" alt=\"\" class=\"wp-image-14420\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38w.png 1485w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38w-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38w-1024x381.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38w-768x286.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-38w-535x199.png 535w\" sizes=\"(max-width: 1485px) 100vw, 1485px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0ec40403d66602cfb87ae75084f721c1\">Example 32. The 2-Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1481\" height=\"556\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13.png\" alt=\"\" class=\"wp-image-14421\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13.png 1481w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13-300x113.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13-1024x384.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13-768x288.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13-535x201.png 535w\" sizes=\"(max-width: 1481px) 100vw, 1481px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1481\" height=\"556\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13w.png\" alt=\"\" class=\"wp-image-14422\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13w.png 1481w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13w-300x113.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13w-1024x384.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13w-768x288.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-13w-535x201.png 535w\" sizes=\"(max-width: 1481px) 100vw, 1481px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-dbb2eb4c3a2dabd74222b3086b7f5162\">Example 33. The 2-Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1484\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03.png\" alt=\"\" class=\"wp-image-14423\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03.png 1484w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03-1024x382.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03-768x287.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03-535x200.png 535w\" sizes=\"(max-width: 1484px) 100vw, 1484px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1484\" height=\"554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03w.png\" alt=\"\" class=\"wp-image-14424\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03w.png 1484w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03w-300x112.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03w-1024x382.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03w-768x287.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-3x3-03w-535x200.png 535w\" sizes=\"(max-width: 1484px) 100vw, 1484px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflection magic squares<\/strong> of order 12 having <strong>8-digits cells entries<\/strong> with 2 numbers combinations (3, 8), (1, 3) and (0, 3). The blocks of order 3 are <strong>semi-magic<\/strong> squares of order 3 with different <strong>semi-magic<\/strong> sums.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(212,193,193) 22%,rgb(18,184,20) 57%,rgb(237,212,212) 74%,rgb(113,206,126) 100%)\">Magic Squares of Order 13<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-60a89780fdb35a1d79d4ce75650cd8dd\">a) 4-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0eb7199fc1a962fcf3440de126012fd9\">Example 34. The 4-Digits (2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1160\" height=\"592\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358.png\" alt=\"\" class=\"wp-image-14431\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358.png 1160w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358-300x153.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358-1024x523.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358-768x392.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358-535x273.png 535w\" sizes=\"(max-width: 1160px) 100vw, 1160px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1160\" height=\"592\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358w.png\" alt=\"\" class=\"wp-image-14432\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358w.png 1160w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358w-300x153.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358w-1024x523.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358w-768x392.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-2358w-535x273.png 535w\" sizes=\"(max-width: 1160px) 100vw, 1160px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-33a86254dfd0b44e1db08105958337a8\">Example 35. The 4-Digits (1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1142\" height=\"593\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235.png\" alt=\"\" class=\"wp-image-14433\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235.png 1142w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235-1024x532.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235-768x399.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235-535x278.png 535w\" sizes=\"(max-width: 1142px) 100vw, 1142px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1142\" height=\"593\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235w.png\" alt=\"\" class=\"wp-image-14434\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235w.png 1142w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235w-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235w-1024x532.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235w-768x399.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-1235w-535x278.png 535w\" sizes=\"(max-width: 1142px) 100vw, 1142px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-809af83694ffe6cc3f593cfadbb62168\">Example 36. The 4-Digits (0, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1158\" height=\"590\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235.png\" alt=\"\" class=\"wp-image-14435\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235.png 1158w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235-300x153.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235-1024x522.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235-768x391.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235-535x273.png 535w\" sizes=\"(max-width: 1158px) 100vw, 1158px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1158\" height=\"590\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235w.png\" alt=\"\" class=\"wp-image-14436\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235w.png 1158w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235w-300x153.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235w-1024x522.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235w-768x391.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0235w-535x273.png 535w\" sizes=\"(max-width: 1158px) 100vw, 1158px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-48e698272d7dd15fcc60dc20e0f91b84\">Example 37. The 4-Digits (0, 1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1100\" height=\"617\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138.png\" alt=\"\" class=\"wp-image-14437\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138.png 1100w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138-300x168.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138-1024x574.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138-768x431.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138-535x300.png 535w\" sizes=\"(max-width: 1100px) 100vw, 1100px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1100\" height=\"617\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138w.png\" alt=\"\" class=\"wp-image-14438\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138w.png 1100w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138w-300x168.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138w-1024x574.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138w-768x431.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-0138w-535x300.png 535w\" sizes=\"(max-width: 1100px) 100vw, 1100px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflection pandiagonal<\/strong> magic squares of order 13 having <strong>4-digits cells entries<\/strong> with 4 numbers combinations (2, 3, 5, 8), (1, 2, 3, 5), (0, 2, 3, 5) and (0,1,3,8). <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-ec61b07d51a39014f30f38c3524f9bd3\">b) 6-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0cfc9cdd4175e30ac4438770a167b6d7\">Example 38. The 3-Digits (2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1524\" height=\"589\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235.png\" alt=\"\" class=\"wp-image-14439\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235.png 1524w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235-1024x396.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235-768x297.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235-535x207.png 535w\" sizes=\"(max-width: 1524px) 100vw, 1524px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1524\" height=\"589\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235w.png\" alt=\"\" class=\"wp-image-14440\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235w.png 1524w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235w-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235w-1024x396.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235w-768x297.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-235w-535x207.png 535w\" sizes=\"(max-width: 1524px) 100vw, 1524px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-b752491bfbfc84a8c60850b1c6c21784\">Example 39. The 3-Digits (1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1450\" height=\"618\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138.png\" alt=\"\" class=\"wp-image-14441\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138.png 1450w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138-1024x436.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138-535x228.png 535w\" sizes=\"(max-width: 1450px) 100vw, 1450px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1450\" height=\"618\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138w.png\" alt=\"\" class=\"wp-image-14442\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138w.png 1450w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138w-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138w-1024x436.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138w-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-138w-535x228.png 535w\" sizes=\"(max-width: 1450px) 100vw, 1450px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a3eef174bd1f8ccf7feaea2cc1fb04a9\">Example 40. The 3-Digits (0, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1450\" height=\"619\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038.png\" alt=\"\" class=\"wp-image-14443\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038.png 1450w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038-768x328.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038-535x228.png 535w\" sizes=\"(max-width: 1450px) 100vw, 1450px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1450\" height=\"619\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038w.png\" alt=\"\" class=\"wp-image-14444\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038w.png 1450w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038w-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038w-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038w-768x328.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-038w-535x228.png 535w\" sizes=\"(max-width: 1450px) 100vw, 1450px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-4fcf3e2fc17f8b770b0e79a1476129e6\">Example 41. The 3-Digits (0, 1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1454\" height=\"620\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013.png\" alt=\"\" class=\"wp-image-14445\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013.png 1454w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013-535x228.png 535w\" sizes=\"(max-width: 1454px) 100vw, 1454px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1454\" height=\"620\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013w.png\" alt=\"\" class=\"wp-image-14446\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013w.png 1454w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013w-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013w-1024x437.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013w-768x327.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-013w-535x228.png 535w\" sizes=\"(max-width: 1454px) 100vw, 1454px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflection pandiagonal<\/strong> magic squares of order 13 having <strong>6-digits cells entries<\/strong> with 3 numbers combinations (2, 3, 5), (1, 3, 8), (0, 3, 8) and (0, 1, 3). <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3077b9d4db17c7dbc5623348fb3d851c\">b) 8-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-9db0dbdd893ba1cc89fccca524ebe389\">Example 42. The 2-Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1605\" height=\"589\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38.png\" alt=\"\" class=\"wp-image-14447\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38.png 1605w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38-1024x376.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38-768x282.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38-535x196.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38-1536x564.png 1536w\" sizes=\"(max-width: 1605px) 100vw, 1605px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1605\" height=\"589\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38w.png\" alt=\"\" class=\"wp-image-14448\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38w.png 1605w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38w-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38w-1024x376.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38w-768x282.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38w-535x196.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-38w-1536x564.png 1536w\" sizes=\"(max-width: 1605px) 100vw, 1605px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-234f8bc5b777d353ac6dd36c40e11a3b\">Example 43. The 2-Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1608\" height=\"589\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13.png\" alt=\"\" class=\"wp-image-14449\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13.png 1608w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13-1024x375.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13-768x281.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13-535x196.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13-1536x563.png 1536w\" sizes=\"(max-width: 1608px) 100vw, 1608px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1608\" height=\"589\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13w.png\" alt=\"\" class=\"wp-image-14450\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13w.png 1608w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13w-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13w-1024x375.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13w-768x281.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13w-535x196.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-13w-1536x563.png 1536w\" sizes=\"(max-width: 1608px) 100vw, 1608px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-844b1262ef42f6bb17b412c29335cffa\">Example 44. The 2-Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1606\" height=\"591\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03.png\" alt=\"\" class=\"wp-image-14451\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03.png 1606w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03-1024x377.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03-535x197.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03-1536x565.png 1536w\" sizes=\"(max-width: 1606px) 100vw, 1606px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1606\" height=\"591\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03w.png\" alt=\"\" class=\"wp-image-14452\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03w.png 1606w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03w-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03w-1024x377.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03w-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03w-535x197.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/13x13-03w-1536x565.png 1536w\" sizes=\"(max-width: 1606px) 100vw, 1606px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflection pandiagonal<\/strong> magic squares of order 13 having <strong>8-digits cells entries<\/strong> with 2 numbers combinations (3, 8), (1, 3) and (0, 3).<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(212,193,193) 22%,rgb(18,184,20) 57%,rgb(237,212,212) 74%,rgb(113,206,126) 100%)\">References<\/h3>\n\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 51%,rgb(152,150,240) 100%)\">Below are references of complete project in 8 parts for the orders 3 to 25. Mainly, it includes three things: <strong>Upside-down, Mirror Looking<\/strong> and <strong>Water Reflection<\/strong> properties of magic squares.<\/p>\n\n\n\n<ol class=\"wp-block-list has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 3 to 6<\/em>, <strong>Zenodo<\/strong>, January 07, 2025, pp. 1-93, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14607070\">https:\/\/doi.org\/10.5281\/zenodo.14607070<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=12610\">Universal and Upside-Down Magic Squares of Order 3 to 6 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14126\">Water Reflexive Magic Squares: Order 3 to 6 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/09\/30\/universal-and-upside-down-magic-squares-of-order-3-to-6\/\">Universal and Upside-Down Magic Squares of Order 3 to 6 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/11\/water-reflexive-magic-squares-order-3-to-6\/\">Water Reflexive Magic Squares: Order 3 to 6 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 7 to 10<\/em>, <strong>Zenodo<\/strong>, January 07, 2025, pp. 1-171, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14607071\">https:\/\/doi.org\/10.5281\/zenodo.14607071<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=12654\">Universal and Upside-Down Magic Squares of Orders 7 to 10 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14213\">Water Reflexive Magic Squares: Order 7 to 10 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/09\/30\/universal-and-upside-down-magic-squares-of-orders-7-to-10\/\">Universal and Upside-Down Magic Squares of Orders 7 to 10 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/11\/water-reflexive-magic-squares-order-3-to-6\/\"><\/a><a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/11\/water-reflexive-magic-squares-order-7-to-10\/\">Water Reflexive Magic Squares: Order 7 to 10 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 11 to 13<\/em>, <strong>Zenodo<\/strong>, January 15, 2025, pp. 1-146, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14649320\">https:\/\/doi.org\/10.5281\/zenodo.14649320<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=12731\">Universal and Upside-Down Magic Squares of Orders 11 to 15 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14339\">Water Reflection Magic Squares: Order 11 to 13 (new site).<\/a> <\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/07\/universal-and-upside-down-magic-squares-of-orders-11-to-15\/\">Universal and Upside-Down Magic Squares of Orders 11 to 15 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-11-to-13\/\">Water Reflection Magic Squares: Orders 11 to 13 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 14 to 16<\/em>, <strong>Zenodo<\/strong>, January 15, 2024, pp. 1-140, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14649519\">https:\/\/doi.org\/10.5281\/zenodo.14649519<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13138\">Universal and Upside-Down Magic and Bimagic Squares of Order 16 (new site) <\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13138\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=14518\">Water Reflection Magic Squares: Order 14 to 16 (new site).<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/16\/universal-and-upside-down-magic-and-bimagic-squares-of-order-16\/\">Universal and Upside-Down Magic and Bimagic Squares of Order 16 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-14-to-16\/\">Water Reflection Magic Squares: Orders 14 to 16 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 17 to 20<\/em>, Zenodo, January 17, 2025, pp. 1-86, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14676293\">https:\/\/doi.org\/10.5281\/zenodo.14676293<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13186\">Universal and Upside-Down Magic Squares of Order 20 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13186\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=14561\">Water Reflection Magic Squares: Orders 17 to 20 (new site)<\/a>.<\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/23\/universal-and-upside-down-magic-and-bimagic-squares-of-order-16-2\/\">Universal and Upside-Down Magic Squares of Order 20 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-17-to-20\/\">Water Reflection Magic Squares: Orders 17 to 20 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 21 to 23<\/em>, <strong>Zenodo<\/strong>, January 20, 2025, pp. 1-83,  <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14688709\">https:\/\/doi.org\/10.5281\/zenodo.14688709<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13242\">Universal and Upside-Down Magic Squares of Order 21 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13242\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=14616\">Water Reflection Magic Squares: Orders 21 to 23 (new site).<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/23\/10984\/\">Universal and Upside-Down Magic Squares of Order 21 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-21-to-23\/\">Water Reflection Magic Squares: Orders 21 to 23 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Order 24<\/em>, <strong>Zenodo<\/strong>, Janeiro 20, 2025, pp. 1-150, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14700325\">https:\/\/doi.org\/10.5281\/zenodo.14700325<\/a>\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13299\">Universal and Upside-Down Magic Squares of Order 24 (new site)<\/a><\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=14668\">Water Reflection Magic Squares: Order 24 (new site)<\/a>.<\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/29\/universal-and-upside-down-magic-squares-of-order-24\/\">Universal and Upside-Down Magic Squares of Order 24 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-order-24\/\">Water Reflection Magic Squares: Order 24 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Order 25<\/em>, <strong>Zenodo<\/strong>, January 21, 2025, pp. 1-79, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14715162\">https:\/\/doi.org\/10.5281\/zenodo.14715162<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13336\">Universal and Upside-Down Magic and Bimagic Squares of Order 25 (new site) <\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14749\">Water Reflection Magic Squares: Order 25. (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/30\/universal-and-upside-down-magic-and-bimagic-squares-of-order-25\/\">Universal and Upside-Down Magic and Bimagic Squares of Order 25 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-order-25\/\">Water Reflection Magic Squares: Order 25 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>This work brings more concepts in magic squares. In past we studied a lot of upside-down and mirror looking magic squares. These are based some kind of digital\/special fonts. To understand better let&#8217;s consider the following 10 digits from 0 to 9: Upside-down (180 degrees rotation) Let&#8217;s make 180 degrees rotation over the above 10 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":14376,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-14339","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-magic-squares"],"jetpack_featured_media_url":"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/12x12-4x4-1235.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14339"}],"version-history":[{"count":16,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14339\/revisions"}],"predecessor-version":[{"id":14794,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14339\/revisions\/14794"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/14376"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}